Optimal Co-linear Gaussian Beams for Spontaneous Parametric Down-Conversion

I investigate the properties of spontaneous parametric down-conversion (SPDC) involving co-linear Gaussian spatial modes for the pump and the photon collection optics. Approximate analytical and numerical results are obtained for the peak spectral density, photon bandwidth, pair collection probability, heralding ratio, and spectral purity, as a function of crystal length and beam focusing parameters. I address the optimization of these properties individually as well as jointly, and find focusing conditions that simultaneously bring the pair collection probability, heralding ratio, and spectral purity to near-optimal values. These properties are also found to be nearly scale invariant, that is, ultimately independent of crystal length. The results obtained here are expected to be useful for designing SPDC sources with high performance in multiple categories for the next generation of SPDC applications.Comment: 15 pages, 8 figures. Corrected normalization coefficient in eqn. 1 and a typo in the definition of wavenumber following eqn. 7. No results were affected by these correction

Counting Abelian Squares for a Problem in Quantum Computing

In a recent work I developed a formula for efficiently calculating the number of abelian squares of length $t+t$ over an alphabet of size $d$, where $d$ may be very large. Here I show how the expressiveness of a certain class of parameterized quantum circuits can be reduced to the problem of counting abelian squares over a large alphabet, and use the recently developed formula to efficiently calculate this quantity

Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission

We present results of a bright polarization-entangled photon source operating at 1552 nm via type-II collinear degenerate spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal. We report a conservative inferred pair generation rate of 123,000 pairs/s/mW into collection modes. Minimization of spectral and spatial entanglement was achieved by group velocity matching the pump, signal and idler modes and through properly focusing the pump beam. By utilizing a pair of calcite beam displacers, we are able to overlap photons from adjacent down-conversion processes to obtain polarization-entanglement visibility of 94.7 +/- 1.1% with accidentals subtracted.Comment: 4 pages, 7 color figures. Revised manuscript includes the following changes: corrected pair generation rate from 44,000/s/mW pump to 123,000/s/mW pump; replaced Fig. 1b to enhance clarity; minor alterations to the title, abstract and introduction; grammatical correction